On the Gross–Pitaevskii equation for trapped dipolar quantum gases
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AbstractWe study the time-dependent Gross-Pitaevskii equation describing Bose-Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension reduction for this nonlinear and nonlocal Schrödinger equation. © 2008 IOP Publishing Ltd and London Mathematical Society.
CitationCarles R, Markowich PA, Sparber C (2008) On the Gross–Pitaevskii equation for trapped dipolar quantum gases. Nonlinearity 21: 2569–2590. Available: http://dx.doi.org/10.1088/0951-7715/21/11/006.
SponsorsThis work has been supported by the KAUST Investigator Award of P Markowich. RC is partially supported by the ANR project SCASEN. PM acknowledges support from the Royal Society through his Wolfson Research Merit Award. CS has been supported by the APART grant of the Austrian Academy of Science.